Consider this equation:%0D%0A%0D%0A4(3x−2)=−24%0D%0A4%0D%0A(%0D%0A3%0D%0A%0D%0A−Part 1. What is your first step in solving this equation? Remember, there is more than one way to solve this equation.%0D%0A%0D%0APart 2. How would you isolate the variable and solve for x after you have completed Part 1?%0D%0A%0D%0AYou do not need to solve the problem. Simply, describe your process.

Question

Consider this equation:%0D%0A%0D%0A4(3x−2)=−24%0D%0A4%0D%0A(%0D%0A3%0D%0A%0D%0A−Part 1. What is your first step in solving this equation? Remember, there is more than one way to solve this equation.%0D%0A%0D%0APart 2. How would you isolate the variable and solve for x after you have completed Part 1?%0D%0A%0D%0AYou do not need to solve the problem. Simply, describe your process.

Answer 1

Part 1: The first step in solving this equation is to distribute the 4 to the terms inside the parentheses. This can be done by multiplying 4 with each term inside the parentheses.

Part 2: After completing Part 1, the equation can be rewritten as 12x - 8 = -24. To isolate the variable x, the next step would be to move the constant term (-8) to the other side of the equation by adding 8 to both sides. This gives us 12x = -24 + 8, which simplifies to 12x = -16. Finally, to solve for x, we would divide both sides of the equation by 12, resulting in x = -16/12, or x = -4/3.

Answer 2

Part 1: The first step in solving this equation is to distribute the 4 to both terms inside the parentheses. This can be done by multiplying 4 with each term inside the parentheses:

4 * 3x = 12x
4 * (-2) = -8

The equation now becomes:
12x - 8 = -24

Part 2: To isolate the variable and solve for x, we need to get rid of the constant term (-8) on the left side of the equation. We can do this by adding 8 to both sides:

12x - 8 + 8 = -24 + 8
12x = -16

Finally, to solve for x, we divide both sides of the equation by 12:

12x/12 = -16/12
x = -4/3

So, the process involves distributing the 4, combining like terms, isolating the variable by getting rid of the constant term, and then solving for x.

Answer 3

To solve the equation 4(3x−2) = −24, the first step is to apply the distributive property by multiplying 4 with each term inside the parentheses. This will give us 12x − 8 = −24.

Now, let's move on to isolating the variable, x. We can do this by getting rid of the constant term, -8, on the left side of the equation. To achieve this, we need to perform the opposite operation, which is adding 8 to both sides of the equation.

By adding 8 to both sides, we get 12x − 8 + 8 = −24 + 8. Simplifying this gives us 12x = -16.

Since we want to solve for x, we need to divide both sides of the equation by the coefficient of x, which is 12. Dividing both sides by 12 gives us (12x)/12 = -16/12. Simplifying this step further, we find x = -4/3.

So, the process to solve the equation involves applying the distributive property first and then isolating the variable by performing inverse operations to eliminate any constant terms and coefficients on the variable's side.